"the most common allele for a given SNP"... in the cohort in question. The cohort may be just 10 people, though, or it could be 2,504 like in 1000 Genomes Phase III. In addition, the major allele, by definition, could have a frequency of 50.5%, in which case, although it is more frequent, it is only more frequent by 0.5%. The point that I want to make is that the major allele only makes sense when you understand the cohort in which it is the major allele, and also the size of that cohort.
As above but, yes, the reverse, in that it is the less frequent allele. Also, yes, the MAF is the frequency of the minor allele and, from the MAF, one can infer the frequency of the major allele if it is a bi-allelic site (some sites understandably are tri- or quad-allelic).
On what you said about the "variation of genotypes", if a site has a very low MAF in a global cohort (i,.e. samples from various parts of the World), it may imply that the major allele is conserved and is 'fixed' in the human genome, but not necessarily. A very rare allele at such a site may, thus, be under selective pressure if it reflects positive gain of function, or it could be deleterious and more likely to be eliminated from the human lineage.
What you said is correct. The risk allele is statistically significantly associated with risk of having a disease under study. Such an allele should have genome-wide significance and have an odds ratio > 1.0. A situation in which a major allele may be seen as the 'risk allele' is where the minor allele is found to be protective against disease by having an odds ratio < 1.0, coupled with a statistically significant p-value. However, such a situation is not usually interpreted from the context of the major allele being the risk allele.
You may have been thinking about rare and common (MAF>5%) variants. For example, it is accepted (by those who actually think) that common alleles have roles in disease. An example are the variants in the CCND1 locus, which have MAFs of ~15% in Caucasians but which confer increased risk of ER+ breast cancer. Look at Rare and common variants: twenty arguments. for further reading.
I should add that many rare variants may be functionless, but that they can still accumulate in the human genome and eventually become functional if combined with other nearby variants. For example, variants accumulated over time eventually form novel TSS sites, TF binding sites, histone binding sites, protein binding sites, etc.
In relation to the above 3, you may enjoy reading a recent answer that I gave: A: SNP dataset and Z Score
This isn't used that much. It is essentially the allele whose effects in relation to disease are being studied. The effect allele is therefore, invariably, the minor allele.
If you hear this term, exercise caution. The best way to view it is as the allele that is in a particular reference build, e.g., GRCh37 / hg19, GRCh38 / hg38, etc. In some cases, however, the reference allele can be a risk allele. Read here for further information: A: Alternate nucleotide is more frequent than reference nucleotide. OMG I'm dizzy.
Not the same as the reference allele. A wildtype allele is specific to your case-control study and is merely the allele that is present in your wild-type samples. This could feasibly be a minor allele, or anything else - it's specific to your study and what you view as the wild-type condition.